Arbitrary and simultaneous control of multiple objects in microfluidic systems

ABSTRACT

In a microfluidic device, respective motion of a plurality of objects along corresponding trajectories is achieved by determining a force field, such as an underlying fluid flow which, when applied to the plurality of object, moves each object along its corresponding trajectory. The force field is a linear superposition of a subset of all force fields supported by the physical characteristics of the microfluidic device. Once the fields have been ascertained, a plurality of actuation signals corresponding to the fields is applied to actuators installed on the microfluidic device to cause the force on each object. By implementing a feedback structure, corrections for positional errors may be made by computing a corrective force for each object and adjusting the actuation signals appropriately thereto.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with support of the United States Government.The United States Government has certain rights in the invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention described herein is directed to the manipulation ofmultiple objects suspended in fluids within microfluidic devices throughthe application of complex force fields. More specifically, the presentinvention is a method for determining and subsequently applying a set ofsignals to one or more actuators on a microfluidic device so as torespectively apply a corresponding force on each of one or more objectscontained therein to thereby manipulate the position, velocity, shape,orientation, and/or distribution thereof.

2. Description of the Prior Art

Microfabrication techniques have been used for over a decade to producea variety of submillimeter mechanical structures. For example, the newfabrication techniques have led the way to the production ofMicro-Electro-Mechanical Systems (MEMS) in which microscopic machinery,sensors, actuators, and electronic circuitry are assembled on, and inmany cases etched from, a common substrate, such as silicon. Many ofthese micromachined devices have enjoyed a wide range of applicabilityin such fields as chemical and biological research.

In certain technological fields, such as the aforementioned chemical andbiological research, the physical scale of certain domains of interesthave motivated the development of sophisticated equipment capable ofmanipulating microscopic objects, both individually and in selectedgroups. One device widely used in this area is the optical tweezer (alsoknown as laser tweezers) which uses laser light to manipulate objects ofmolecular size scales. Optical tweezers create an optical trap on anobject through light scattering forces and light intensity gradientforces of a focused laser beam. The forces combine to hold the object inthe center of the focused laser spot. The trapped object may berepositioned by moving the focused laser spot as desired.

Optical tweezers are effective in manipulating certain types of objects,but suffer several shortcomings which prevent their implementation in awider range of applications. Optical tweezers can be used to manipulateparticles, provided there is a difference in the index of refraction ofthe particle and that of the surrounding medium, but have yet to be usedeffectively to redistribute fluids. Manipulation of fluids on amicroscopic scale has become a useful method in delivering chemicalagents to individual cells to observe how the cells react thereto.

Another shortcoming of optical tweezers is that they are large andgenerally expensive pieces of equipment. In typical applications, alaser tweezer will consist of one or more lasers, a microscope, andhigh-quality focusing optics to produce each optical trap.

Manipulation of submillimeter objects by electrophoresis and othermethods using an applied electric field have been used for many years.Electrophoresis has been widely used for separating and sortingparticles into bands in accordance with particle size and inherentelectric charge. Gel electrophoresis, for example, whereby an electricfield is applied to molecules suspended in a porous gel, is used in thefield of genetics for DNA profiling. However, while electrophoresis isuseful for applying a force on certain particles, such as molecules, theprocess is not operative on objects immovable by an electric field, suchas objects made of a dielectric material. Additionally, electrophoresismay be used to sort particles according to a charge/size ratio intosorting bins located along a straight path, but does not provide a meansfor steering the objects toward alternative locations not on the path.

Sorting of minute particles is a prevalent requirement in many researchand biochemical fields, and many means for performing this task arewidely available. For example, one common application passes a stream ofparticles suspended in an electrolyte through a small aperture overwhich an electric field is applied. A particle in the aperture displacesan amount of electrolyte equal to its own volume. In accordance with theCoulter principle, the volume displaced changes the impedance of theaperture and is measured as a voltage pulse, the height of which isproportional to the volume of electrolyte displaced, i.e., the volume ofthe particle. The particles may then be sorted by size by deflectingdifferent sized particles into a corresponding sorting location or bin,by some mechanism such as an optical tweezer. The Coulter particlesorter illustrates the benefits of device implementation on amicromachined platform, i.e., to measure a change in impedance in achannel or aperture caused by the presence of a microscopic particle,the channel or aperture is required to be formed on a size scalecomparable with the size of the particle.

An illustrative example of another cell sorting device constructed bymicromachined techniques is provided by the journal article, “AnIntegrated Microfabricated Cell Sorter,” by Anne Fu, et al. (AnalyticalChemistry, Vol. 74, No. 11, Jun. 1, 2002). The referenced cell sorterimplements a network of microvalves and micropumps for controlling themovement of cells suspended in a fluid after the classification thereofby controlling the surrounding fluid flow. Cells within the device areclassified by means of fluorescence of the cell resulting fromexcitation by an argon laser. Various valves and pumps are activated inaccordance with one of a number of predetermined patterns so as todirect a particle to a destination sorting bin by directing the flow ofthe suspending fluid along one of a number of predetermined paths.However, the geometry of the fluid channel and the pump and valveconfiguration allow only a limited control over the motion of anyparticular cell. Moreover, the configuration does not affordsimultaneous parallel control of multiple particles within the fluid.For example, the device does not contemplate directing different objectstoward each other.

Particle placement and sorting are not the only tasks for whichmicroscopic object manipulation means are desired. Many applicationsrequire the manipulation of fluids on a microscopic scale for purposesof, for example, mixing, dosing, and delivering small quantities of drugto individual cells. In other applications, objects such as strandsrequire shape orientation or conformation. For example, in certainapplications, DNA strands may need to be “unwrapped” to expose certainstructural features for study. To perform these functions, complexmotion of multiple particles, strand segments and surfaces is necessary.However, simultaneous arbitrary control of the trajectories of multipleobjects presents a challenging controller design problem.

One device for controlling the motion of multiple objects is theUniversal Planar Manipulator (UPM) developed by Dan Reznik, formerly ofthe University of California at Berkeley. Objects to be manipulated areplaced on a rigid, horizontally oriented plate. The plate is coupled toone or more actuators which vibrates the plate in the horizontal plane.The objects are moved by means of frictional forces selectively overcomeor engaged by the acceleration of the vibrating plate.

The control of motion of the objects on the UPM is achieved through aclosed loop configuration consisting of a camera, for photographing thehorizontal plate and the objects thereon, a set of motors for vibratingthe plate and a computer for a) determining the positions of the objectsat each sampling interval, b) computing the forces to be applied to eachobject so that the object follows its predesignated trajectory, c)computing the motion of the plate which will bring about all of therequired forces, and d) applying a signal to each actuator so as to movethe plate in the required manner. The process is repeated periodicallyaccording to a predetermined sampling schedule.

The UPM control method determines, at each sample period, a center ofrotation (COR) about which the plate is to be rotated and the magnitude(i.e., duration) of the rotation. By strategically placing the COR ateach sampling period, the required forces are generated, in atime-averaged sense, so as to move the objects in their respectivelyassigned trajectories.

Whereas the UPM illustrates that parallel control of multiple objects ona common medium is possible, its method of control cannot be applied tosystems where gravity has much less influence on the objects than doother forces. For example, in fluidic realms, the effects of turbulenceand fluid viscosity are as significant as those due to gravity. Fluidflow, in general, is a complex process presenting exceptional controlchallenges. Some of the unwanted effects of turbulence may be mitigatedby controlling the fluid on a small size scale where the momentum of thefluid reaches negligibility. However, the control of fluid flow byacceleration (i.e., by relying on gravitational forces) on such sizescales becomes highly impractical.

As shown by consideration of the shortcomings of the prior art, there isan apparent need for parallel control of multiple objects suspended orimmersed in a fluid such that each object follows an arbitrarytrajectory.

SUMMARY OF THE INVENTION

One aspect of the present invention provides a method for transportingobjects suspended in a fluid respectively along correspondingtrajectories. A microfluidic receptacle is provided to contain the fluidand the objects suspended therein. The microfluidic receptacle includesa plurality of actuators installed thereon for creating a force fieldwithin the microfluidic device. The force field respectively imparts acorresponding force on each of the objects. The microfluidic receptaclefurther includes a sensor for determining at least the location of eachobject therein. A plurality of force fields defining forces on theobjects responsive to a set of actuation signals is determined for themicrofluidic receptacle. The method of the present invention thendetermines, at each sampling interval, a destination point on atrajectory corresponding to each object. The method selects a set offorce fields from the plurality of force fields for producing the forceson each object to transport it along its corresponding trajectory. Aplurality of actuation signals corresponding to the set of fields isselected and respectively applied to each actuator so as to produce thetotal force field. Once the signals have been applied to the actuators,the method is repeated until all of the objects have traversed theircorresponding trajectories.

Another aspect of the present invention provides a method fortransporting a plurality of particles suspended in a fluid respectivelyalong a corresponding one of a plurality of trajectories. A microfluidicreceptacle is provided to receive the fluid in which the particles aresuspended. The microfluidic receptacle includes a plurality of fluidactuators installed thereon for respectively applying a correspondingforce on the fluid. A plurality of fluid flow fields defining the fluidflow responsive to a set of actuation signals is determined for themicrofluidic receptacle. The method of the present invention thendetermines, at each sampling interval, a destination point on atrajectory corresponding to each particle. The method selects a set offluid flow fields from the plurality of fluid flow fields for producingthe fluid flow to transport each particle along its trajectory. Aplurality of actuation signals corresponding to the set of fluid flowfields is selected and respectively applied to each fluid actuator so asto produce the flow. Once the signals have been applied to the fluidactuators, the method is repeated until all of the particles havetraversed their corresponding trajectories.

In a further aspect of the present invention, a method is provided forsorting a plurality of particles suspended in a fluid in accordance withan attribute possessed by the particles. In this aspect of the presentinvention, the microfluidic receptacle includes a plurality of fluidactuators, a sensor to detect the position and attribute of eachparticle within the fluid, and a plurality of sorting bin locations forreceiving particles having a corresponding attribute. A plurality offluid flow fields defining the fluid flow responsive to a set ofactuation signals is determined for the microfluidic receptacle. Themethod of the present invention then determines the attribute of eachparticle via the sensor at each sampling interval. The method thenestablishes a plurality of trajectories, one for each particle, whichdirects the particle to the sorting bin location receiving particles ofthe associated attribute. The method selects a set of fluid flow fieldsfrom the plurality of fluid flow fields that produces a fluid flow suchthat each particle is moved toward its corresponding sorting binlocation. The method then selects the actuation signals to be applied tothe actuators so that the fluid flow is produced and, once the signalshave been applied, repeats the method until each of the particles hasarrived at its corresponding sorting bin location.

In a further aspect of the present invention, a method is provided forconforming a strand from a first conformation to a second conformation,where the strand is suspended in a fluid. The microfluidic receptacle isprovided with a plurality of fluid actuators and a sensor to detect aposition of a plurality of strand segments forming the strand. Aplurality of fluid flow fields defining the fluid flow responsive to aset of actuation signals is determined for the microfluidic receptacle.Once the respective position of each of the strand segments has beendetermined by sensor, a plurality of trajectories, one for each of thestrand segments, is established and is directed to a correspondingsegment position of that segment in the second conformation of thestrand. The method selects a set of fluid flow fields from the pluralityof fluid flow fields for that produces a flow that moves the strandsegments toward the second conformation segment position. A plurality ofactuation signals corresponding to the selected fluid flow fields isapplied to the fluid actuators, and the method is repeated until each ofthe strand segments has arrived to its strand segment location in thesecond strand conformation.

In yet another aspect of the present invention, a method is provided forredistributing a first volume of fluid from a first distribution to asecond distribution, where the first volume of fluid is immersed withina second volume of fluid and is separated therefrom by at least onefluid interface. The microfluidic receptacle is provided with theplurality of fluid actuators and a sensor to detect a position of afirst plurality of segments defining the at least one fluid interface. Aplurality of fluid flow fields defining the fluid flow responsive to aset of actuation signals is determined for the microfluidic receptacle.Each of the first plurality of interface segments is located via thesensor and a plurality of trajectories is established, each directed toa corresponding interface segment location defining the seconddistribution of fluid. A set of fluid flow fields is selected from theplurality of fluid flow fields that produces a fluid flow such that theplurality of segments is directed along its corresponding trajectory. Aplurality of actuation signals corresponding to the selected fluid flowfields is applied to the plurality of fluid actuators and the method isrepeated until the first plurality of interface segments has arrived atthe corresponding one of the plurality of interface segments of thesecond distribution of the first fluid.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a sorting operation as performed by anexemplary microfluidic device;

FIG. 2A is an illustration of the construction of an exemplaryelectro-osmotic microfluidic device;

FIG. 2B is a cross-sectional view and functional illustration of theelectro-osmotic device of FIG. 2A;

FIG. 3 is an illustration of an exemplary discrete sample space of themicrofluidic chamber of the electro-osmotic device;

FIG. 4 is an illustration of a fluid flow field for the exemplaryelectro-osmotic device;

FIGS. 5A-5B are graphs of relative strengths of a given eigenmode to thefirst eigenmode of the exemplary electro-osmotic device;

FIGS. 6A-6F illustrate various fluid flow fields of the exemplaryelectro-osmotic device;

FIG. 7 is a block diagram of an exemplary system on which the method ofthe present invention may be deployed;

FIG. 8 is a block diagram of exemplary functional components forexecuting the method of the present invention;

FIG. 9 is a control diagram of an exemplary embodiment of the presentinvention;

FIG. 10 is a flow chart of an exemplary embodiment of the method of thepresent invention;

FIGS. 11A-11D are illustrations depicting motion of a plurality ofparticles as conducted by the method of the present invention;

FIGS. 12A-12D illustrate examples of object manipulation by the methodof the present invention;

FIGS. 13A-13B illustrate an exemplary fluid distribution experiment asimplemented by the method of the present invention;

FIG. 14 is an illustration of a system configuration whereby amicroscope is implemented as the sensing means for an exemplaryembodiment of the present invention;

FIG. 15 is a histogram illustrating an exemplary image thresholdselection method as implemented by exemplary embodiments of the presentinvention;

FIG. 16 is an illustration of exemplary post-threshold pixel data of anobject for demonstrating run length coding image processing of exemplaryembodiments of the present invention;

FIG. 17 is an illustration of object detection as implemented byexemplary embodiments of the present invention; and

FIG. 18 is a flow chart depicting pertinent steps in an object detectionprocess of exemplary embodiments of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Prior to discussing the exemplary embodiments of the present invention,it is believed as beneficial to briefly define certain terminology asused throughout this Application for Patent. For purposes of thefollowing, a “force field” is intended to mean a set of forces in aregion of space imparting a total force vector on an object as afunction of the object's position in the region of space. In this sense,force fields include, but are not limited to, electric fields in aregion, magnetic fields in a region and fluid flow fields in a region.

The term “fluid” is meant to refer to non-solid media including, but notlimited to, gases, liquids and gels.

The term “microfluidic” refers to properties of, and processes on,fluids constrained to regions of a physical size scale wherein inertialeffects of the fluid are much less than the viscous effects thereof,i.e., a flow having a vanishingly small Reynolds number. Additionally,gravitational forces on the fluid at the physical size scale arenegligible. Typically, the size scale of a microfluidic process orsystem is less than 1 mm.

An “object” is to be understood as an inanimate (i.e., notself-propelling) particle of arbitrary shape, an inanimate chain orstrand or a region of space occupied by a fluid.

Object “conformation” is to be understood as any aspect of an object'sinternal or external shape or orientation. Additionally, conformationrefers to an object's internal or external physical state (e.g.temperature, shear stress, etc.).

An “actuator” refers to a means for generating a force field within aregion of space. This includes, but is not limited to, electrodesforming electric and magnetic fields, means for applying forces onfluids by, for example, pressure, electrical, magnetic orelectromagnetic fields, thermal processes, surface tension, orelectro-osmosis.

A “force field eigenmode” (or alternatively, simply “eigenmode”) is acharacteristic force field within a microfluidic channel or receptacleas constrained by the channel geometry, actuation type, and actuatorplacement.

Referring now to FIG. 1, there is shown, in simplified form, anexemplary microfluidic device 100 for illustrating certain fundamentalconcepts of the present invention. In the embodiment of FIG. 1,microfluidic device 100 is configured to perform a sorting operation,which is a useful configuration for purposes of illustrating the basicconcepts. Whereas the Figure shows the microfluidic device 100 to be ofa particular shape and being fitted with actuators of a particular type,the exemplary configuration of FIG. 1 is meant to be illustrative andnot restrictive. The method of the present invention is independent of aparticular geometry and actuator type.

In the example of FIG. 1, a plurality of particles 120, 130, 140 havingvaried attributes have been introduced into channel 102 by means of asuspending fluid. The objective of the sorting operation is to transportparticles 120 to sorting bin location 104 a, particles 130 to sortingbin location 104 b, and particles 140 to sorting bin location 104 c.Whereas, the sorting bin locations 104 a-104 c are shown in FIG. 1 asphysically separated ports, the sorting bins may also be simply aseparated region of microfluidic device 100 in which particles of acertain type are congregated.

At periodic time intervals, i.e., once every sampling period, thepositions of each of the particles within the fluid channel 102 aresensed by a particle position sensor, such as by exemplary methodsdiscussed in paragraphs that follow. From each of these particlelocations, a local particle trajectory is computed to set each particleon a path towards its corresponding sorting bin location 104 a-104 c. Bymeans of the present invention, it is then determined what local forcefield vector would cause a corresponding force on the particle so thatthe particle is conducted along its corresponding trajectory. The forcemay be, for example, an electric or magnetic field or may be a flowvector of the fluid in contact with the object. For purposes ofdescription, the latter of the fields is assumed.

As is shown in the Figure, microfluidic device 100 is adapted to receivea plurality of actuators 106 a-106 h. The actuators 106 a-106 h areindependently operated to produce a local fluid current flow about itscorresponding location. It is an object of the present invention torespectively apply an appropriate signal to each actuator 106 a-106 h toproduce an underlying current flow of the fluid suspending particles120, 130, 140 so that the force applied to each particle isapproximately equal to the force required to transport that particularparticle along its corresponding trajectory.

It should be clear from the simplified diagram of FIG. 1 that control ofthe suspending fluid defines the controllability of each of thesuspended particles. In a microfluidic channel, the size of themicrochannel 102 minimizes the effects of inertia of the fluid. Thus, across-channel flow as created by one of actuators 106 a-106 h will notbe sustained beyond the time the actuator is applying a force to thefluid. Turbulent flows are thereby minimized and the particle followsthe trajectory as influenced by the fluid flow in an approximatelylinear fashion.

By way of example, the system of FIG. 1 illustrates an object of thepresent invention, namely the control of objects held within amicrofluidic system. As previously stated, the objects are controlled byforces exerted thereon through the force field, which, in the example ofFIG. 1 is through the flow of the surrounding fluid as created by thefluid actuation mechanism. The method of the present invention may beused on a wide variety of microfluidic devices implementing a widevariety of actuation mechanisms.

The present invention provides a method by which multiple objects withina microfluidic receptacle may be respectively transported alongcorresponding trajectories. A microfluidic receptacle of a givengeometry and having a given actuation mechanism (e.g., a complexelectric field generated by a plurality of electrodes or a complex fluidflow generated by pumps or other means described below) is capable ofsupporting a set of force fields therein. As will be shown in paragraphsthat follow, selecting a subset of supported force fields providesstable, parallel control of the motion of the objects within themicrofluidic receptacle.

To implement the present invention, a model of the forces on the objectscontained within a microfluidic system provides insight as to hoe theforce fields supported by the device may be used in the control methodof the present invention. Once the supported force fields have beenascertained, they may be subsequently selected and combined to controlthe motion of the objects. An exemplary embodiment of the presentinvention is now presented in a microfluidic system implementing anelectro-osmotic actuation mechanism.

The fluid flow in any microfluidic system having a minimum device lengthwell above the mean free path of the molecules composing the fluid canbe accurately modeled by the Navier-Stokes equations: $\begin{matrix}{{\nabla{\cdot v^{*}}} = 0} & (1) \\{{\rho( {\frac{\partial v^{*}}{\partial t^{*}} + {v^{*} \cdot {\nabla v^{*}}}} )} = {{- {\nabla P}} + {\eta^{*}{\nabla^{2}v^{*}}}}} & (2)\end{matrix}$where v* is the fluid velocity field, ρ* is the density, P* is thepressure, η* is the viscosity. Here the asterisk denotes dimensionalquantities.

For the microfluidic devices of interest, inertial effects arenegligible compared to the effects of viscosity and Equation (2) maythen be reduced to: $\begin{matrix}{\frac{\partial v^{*}}{\partial t} = {{- \frac{1}{\rho}}( {{\nabla P^{*}} - {\eta{\nabla^{2}v^{*}}}} )}} & (3)\end{matrix}$

It is thus apparent from Equation (3) that a change in the fluid flowfield may be brought about by either a gradient in the pressure of thefluid or by viscous coupling to a moving object (since inertia isminimal at these scales). It is the choice of actuation and acorresponding choice in microfluidic channel geometry that defines thecontrollability of the fluid flow. Equation (3) may thus be used toderive a set of control equations once the geometry and actuationmechanism for a particular microfluidic application have been chosen.

An exemplary embodiment of the electro-osmotic microfluidic device isillustrated in FIGS. 2A-2B. The microfluidic device 200 is constructedfrom a pair of parallel, non-conducting plates 205, 207 separated by adistance h. Passing through both plates and simultaneously isolatedtherefrom is a plurality of electrodes 203, which, as will be shownbelow, provides an electrically motivated viscous coupling to the fluidwhich serves as the exemplary actuating mechanism.

When an aqueous (polar) fluid, such as water, is introduced to themicrofluidic chamber 220, an electrical double layer of ions, commonlyreferred to as the Debye layer, is formed at the plate/liquid interfaceas is shown in FIG. 2B. The Debye layer is caused by such mechanisms asionization, ion adsorption, and ion dissolution. The plurality of thecharge depends on the material used for manufacturing the plates. Whenan electric field, E, is applied along the chamber, i.e., parallel tothe plate surface, the Debye layer is displaced. The displaced Debyelayer moves in accordance with the electric field and the fluid adjacentto the charge layer is “dragged” thereby through viscous coupling. Thisis the process commonly referred to as electro-osmotic flow. Note thatany free floating ions within the fluid contribute a small amount to themotion of the fluid, such motion being a system noise component whichmay be overcome by control techniques, as will be discussed below.Moreover, the particles contribute to Brownian noise of the motion of anobject, which places a lower bound on the size of the target object(i.e. the smaller the object, the greater is the degree to whichBrownian noise influences the motion of the object). The Brownian noiseis may also be overcome by control techniques such as those describedbelow.

When a small object 210 is placed in the microfluidic chamber 220 ofmicrofluidic device 200, the trajectory thereof follows the local fluidflow of the suspended fluid. Thus, as will be detailed in paragraphsthat follow, the trajectory of object 210 may be controlled by selectiveapplication of an electric potential on one or more of the plurality ofelectrodes 203. The electric field produces a corresponding fluidvelocity field serving as the exemplary force field.

The Debye layer thickness, h_(D), (10 nm in most cases) is very smallcompared to the chamber dimensions (1 cm×1 cm×0.05 mm in the exemplarydevice), the boundary conditions at the walls are accurately captured bythe velocity slip conditions, $\begin{matrix}{{v_{wall}^{*}( {x^{*},y^{*},{z^{*} = {{\pm h^{*}}/2}}} )} = {\frac{ɛ^{*}\xi^{*}}{\eta^{*}}{\nabla{\Phi^{*}( {x^{*},y^{*}} )}}}} & (4)\end{matrix}$where ε* is the permittivity of the fluid and ξ* is the zeta potentialat the wall. The electric potential Φ* satisfies the Laplace equation∇(ε*∇Φ*)=0  (5)with the boundary conditions of the applied voltage at the i^(th)control electrode given byΦ*(δD _(i))=u _(i)*  (6)where u_(i)* is the electric potential of the i^(th) electrode, andδD_(i) denotes the electrode surface.

If the viscosity and surface properties are uniform and the fluidvelocity at the inlets is given by (7): $\begin{matrix}{v_{inlet}^{*} = {\frac{ɛ^{*}\xi^{*}}{\eta^{*}}{\nabla\Phi_{inlet}^{*}}}} & (7)\end{matrix}$then the quasi-steady state solution to partial differential equations(1) and (2) is simply given by $\begin{matrix}{{v^{*}( {x^{*},y^{*},z^{*}} )} = {{- \frac{ɛ^{*}\xi^{*}}{\eta^{*}}}{{\nabla{\Phi^{*}( {x^{*},y^{*}} )}_{z}}.}}} & (8)\end{matrix}$showing that the velocity profile is uniform in the vertical z direction(perpendicular to plates 205 and 207). Though the condition (7) is notsatisfied at the surface of the electrodes (at the electrode surface thevelocity should vanish to zero due to no-slip boundary conditions), theflow field relaxes to satisfy this condition within a few lengths of thechannel height from the electrode surfaces and so (8) can be used topredict the fluid velocity in the domain except very near to theelectrode surfaces.

The condition on how slowly the electrode voltages can be varied for thefluid flow to maintain a quasi-steady state should be determined toensure controllability. The time required for the fluid flow in theexemplary device filled with water (ρ*=1000 kg/m³, v*=1 mm/s, h*=0.05mm, η*=0.001 Ns/m²) to reach the steady state of (8) in response to astep voltage input has been determined to be on the order of 1 μs. Thus,if the electric field is varied such that the time period of the highestfrequency input voltage is much greater than 1 μs, the velocity of thefluid at all times may be given by (8).

The motion of an object within the fluid follows the motion of the fluidlocal to the object. Thus, at any time t, the velocity of the j^(th)object at position p_(j)*=(x_(j)*, y_(j)*) is given by $\begin{matrix}{{\frac{\mathbb{d}}{\mathbb{d}t}p_{j}^{*}} = {{v^{*}( p_{j}^{*} )} = {\nabla{\Phi^{*}( p_{j}^{*} )}}}} & (9)\end{matrix}$

For convenience, the dimensionalized equations above may benon-dimensionalized as follows. Since the numerical values of x*, y*,|p_(j)*| are of the order of L*; and Φ*, u* are of the order of|u_(max)*| and |v_(max)*| is of the order of |v_(max)*|, the relations$\begin{matrix}{{{\Phi = \frac{\Phi^{*}}{u_{\max}^{*}}},{v = \frac{v^{*}}{v_{\max}}},{x = \frac{x^{*}}{L^{*}}},{y = \frac{y^{*}}{L^{*}}},{z = \frac{z^{*}}{h^{*}}}}{{p_{j} = \frac{p_{j}^{*}}{L^{*}}},{u_{i} = \frac{u_{i}^{*}}{u_{\max}^{*}}}}{{v_{\max}} = {{\frac{ɛ^{*}\xi^{*}}{\eta^{*}}{\nabla\Phi^{*}}} = \frac{ɛ^{*}\xi^{*}u_{\max}^{*}}{\eta^{*}L^{*}}}}} & (10)\end{matrix}$can be used to write the equations of the system in dimensionlessvariables as∇²Φ=0  (11)v=∇Φ  (12){dot over (p)} _(j) =v(p _(j))  (13)with boundary conditionsΦ(δD _(i))=u _(i)  (14)

The non-dimensionalized system of equations (11), (12), and (14) arelinear and contain no time derivatives, so at any time t the velocityfield v can be expressed as a superposition of velocity fields ∇Φ_(i)(1,2, . . . , n) as follows $\begin{matrix}{{v( {x,{y;u}} )} = {{\nabla{\Phi( {x,{y;u}} )}} = {\sum\limits_{i - 1}^{n}{u_{i}{\nabla{\Phi_{i}( {x,y} )}}}}}} & (15)\end{matrix}$where Φ_(i) solves∇²Φ_(i)=0  (16)with boundary conditionsΦ(δD _(i))=1, Φ(δD _(j))=0, j≠i  (17)where n is the number of electrodes and u=[u₁ u₂ . . . u_(n)] representsthe vector of electrode voltages. An exemplary velocity field ∇Φ isshown in FIG. 3.

Now, since u and u−c (c being some arbitrary constant) generate the samevelocity field v, a vector u may always be chosen such that a particularelectrode voltage is always 0. In other words any achievable velocityfield can be expressed as a linear superposition of any n−1 fields outof ∇Φ_(i) (i=1, 2, . . . , n) which constitute a linearly independentset. Hence we can rewrite (15) as $\begin{matrix}{{v( {x,{y;u}} )} = {{\nabla{\Phi( {x,{y;u}} )}} = {\sum\limits_{i = 1}^{n - 1}{u_{i}{\nabla{\Phi_{i}( {x,y} )}}}}}} & (18)\end{matrix}$

If at time t, the objects are at positions p₁=(x₁, y₁), p₂=(x₂, y₂), . .. , p_(m)=(x_(m), y_(m)), then the velocity of the j^(th) object isgiven by $\begin{matrix}{{\overset{.}{p}}_{j} = {{v( p_{j} )} = {{\nabla{\Phi( p_{j} )}} = {{\sum\limits_{i = 1}^{n}{u_{i}{\nabla{\Phi_{i}( p_{j} )}}}} = {{A( p_{j} )} \cdot u}}}}} & (19)\end{matrix}$

Let v_(1D), v_(2D), . . . , v_(mD) be the desired object velocities attime t. It is desired to proportionally combine the velocity fields∇Φ_(i) so that the fluid velocities at p₁, p₂, . . . , p_(m) are asclose to v_(1D), v_(2D), . . . , v_(mD) as possible. Such a voltagevector u_(opt) can be obtained by solving the least squares problem$\begin{matrix}{{\min{{v_{D} - {A \cdot u_{opt}}}}_{2}}{where}{v_{D} = \lbrack {v_{1D}v_{2D}\ldots\quad v_{mD}} \rbrack^{T}}{u_{opt} = {\lbrack {u_{1{opt}}\quad u_{2{opt}}\ldots\quad u_{nopt}} \rbrack^{T}\quad{and}}}} & (20) \\{{A\lbrack p\rbrack} = \begin{bmatrix}{\nabla{\Phi_{1}( p_{1} )}} & {\nabla{\Phi_{2}( p_{2} )}} & \cdots & {\nabla{\Phi_{n}( p_{1} )}} \\{\nabla{\Phi_{1}( p_{2} )}} & \vdots & \cdots & \vdots \\\vdots & \vdots & \ddots & \vdots \\{\nabla{\Phi_{1}( p_{m} )}} & {\nabla{\Phi_{2}( p_{m} )}} & \cdots & {\nabla{\Phi_{n}( p_{m} )}}\end{bmatrix}} & (21)\end{matrix}$the analytical solution of which is given byu _(opt) =[A ^(T)(p)A(p)]⁻¹ A(p)v _(D).  (22)

When 2m is less than n−1 (i.e., when the twice the number of objects isless than one less than the number of actuators), Equation (22)constitutes an underdetermined system of linear equations which hasmultiple solutions. The least square optimal solution is that with thesmallest norm which allows the required velocities to be reached withminimal applied voltage. Ideally, the optimal solution generates therequired velocity field by combining the lowest order eigenmodes of theavailable force field eigenmodes. The higher eigenmodes require largevoltage components in the solution u_(opt) while having an insignificantimpact on v_(D). As a result, small changes in v_(D) introduces largechanges in u_(opt). This instability imposes significant obstacles inthe control of the fluid and thereby the motion of the objects suspendedtherein.

Increasing the number of objects imposes other restrictions on thevelocity field, i.e., higher eigenmodes of the velocity field must beevoked. Thus, attempting to overcome the control deficiencies by addingactuators to the system fails to do so. To stabilize the system, only asubset of the force field eigenmodes are implemented in the controlmethod, by way of the present invention, as will now be discussed.

Methods for suppressing the higher eigenmodes and to stabilize the leastsquares solution are widely known. For example, Tikhonov regularizationworks by solving the modified problem, $\begin{matrix}{\min\{ {{{v_{D} - {{A(p)}u_{opt}}}}_{2}^{2} + {\lambda^{2}{u_{opt}}_{2}^{2}}} \}} & (23)\end{matrix}$

Another optimization method is TSVD (truncated singular valuedecomposition), which as the name suggests, works by expressing thesolution space as a superposition of only a finite number the lowereigenmodes and discarding the higher eigenmodes of the system. Incertain embodiments of the present invention, TSVD is utilized to selectthe set of implemented force field eigenmodes. From the solution ofEquation (15), $\begin{matrix}{{v( {x,{y;u}} )} = {\sum\limits_{i = 1}^{n}\quad{u_{i}{\nabla{\Phi_{i}( {x,y} )}}}}} & (24)\end{matrix}$on a set of discrete q×q rectangular grid points r_(i) in the domain,where q is chosen such that the grid may resolve the fluid velocityfield sufficiently. Thus, $\begin{matrix}{{{{v( r_{i} )} = {{{D(r)}u\quad i} = 1}},2,{\ldots\quad q^{2}}}{{where},{{D(r)} = \begin{bmatrix}{\nabla{\Phi_{1}( r_{1} )}} & \cdots & {\nabla{\Phi_{n}( r_{1} )}} \\{\nabla{\Phi_{2}( r_{2} )}} & \cdots & \vdots \\\vdots & \vdots & \vdots \\\vdots & \vdots & \vdots \\{\nabla{\Phi_{1}( r_{q}^{2} )}} & \vdots & {\nabla{\Phi_{n}( r_{\quad_{q}^{2}} )}}\end{bmatrix}}}} & (25) \\{{v = \begin{bmatrix}{v( r_{1} )} \\{v( r_{2} )} \\\vdots \\\vdots \\{v( r_{q}^{2} )}\end{bmatrix}},{u = \begin{bmatrix}u_{1} \\\vdots \\u_{n}\end{bmatrix}}} & (26)\end{matrix}$

-   -   where r_(i) denotes the position vector of the i^(th) grid point        as shown in FIG. 3 (q=50). Note that the matrix D(r) is the        discrete-space representation of the matrix A(p). The matrix D        is then decomposed using singular value decomposition so that        $\begin{matrix}        {{D = {M \times \Omega \times N^{T}}}{where}{M = \lbrack {M_{1}\quad M_{2}\ldots\quad M_{n}} \rbrack}{\Omega = \begin{bmatrix}        \sigma_{11} & 0 & 0 & 0 \\        0 & \sigma_{22} & 0 & 0 \\        0 & 0 & \ddots & 0 \\        0 & 0 & 0 & \sigma_{nn} \\        0 & 0 & 0 & 0 \\        0 & 0 & 0 & 0        \end{bmatrix}}{N = {\lbrack {N_{1}N_{2\quad}\ldots\quad N_{m}} \rbrack.}}} & (27)        \end{matrix}$

The i^(th) force field (fluid flow) eigenmode is then given byE _(i)=Σ_(j=1) ^(n) N _(ji)∇Φ_(j)(x,y)

The TSVD forces the column vectors M and N to satisfy:∥M _(i)∥₂=1 and ∥N_(i)∥₂=1  (28)Thus, the application of unit voltage vector N_(i) produces a unitvelocity field vector M_(i) amplified by σ_(ii). The ratio σ₁₁/σ_(ii)indicates the strength of the first mode of the velocity field incomparison to the i^(th) mode when a voltage vector of identicalstrength is applied to the corresponding electrodes of the exemplarydevice in both cases. This ratio is illustrated in FIG. 5A, which showsthat the effect of higher order modes do not influence the flow field asmuch as the lower order modes. As such, only a limited number ofeigenmodes need be implemented.

As previously discussed, the control of the motion of objects within themicrofluidic device is stabilized by selecting a subset of possibleeigenmodes for implementation. If the subset of is chosen as keigenmodes, k≦m, a new matrix, Ñ can be constructed from the first kcolumns of N. Then, a new matrix, Ã, may be formed from the originalmatrix A such that,Ã(p)=A(p)Ñ[Ñ ^(T) Ñ] ⁻¹ Ñ ^(T),  (29)and, then,{dot over (p)}=Ã(p)·u.  (30)The actuator signals for the stabilized control method is then given by,u _(D) =[Ã ^(T)(p)Ã(p)]⁻¹ Ã(p)v _(D)  (31)where u_(D) is the stabilized actuator input corresponding to thedesired force field, v_(D).

A further design consideration lies in the number of actuators toimplement. As previously stated, only the lower order fluid floweigenmodes contribute significantly to the fluid flow. As such, asmaller number of actuators (electrodes in the exemplary device) need beinstalled. This is shown in the graph of FIG. 5B, where the ratioσ₁₁/σ_(ii) is shown for both a 40 electrode device and a 20 electrodedevice. Thus, in certain embodiments of the present invention where thenumber of objects being controlled is less than number of eigenmodesrequired to control those objects, the number of actuators may bedecreased accordingly.

FIGS. 6A-6F illustrate the fluid flow in accordance with a correspondingeigenmode. FIG. 6A illustrates eigenmode 1 (i=1), FIG. 6B illustrateseigenmode 3 (i=3), FIG. 6C illustrates eigenmode 7 (i=7), FIG. 6Dillustrates eigenmode 10 (i=10), FIG. 6E illustrates eigenmode 14(i=14), and FIG. 6F illustrates eigenmode 18 (i=18). It should be clearfrom these Figures how a prudent combination of fluid flow eigenmodesinfluences the local fluid flow and, thereby, the objects suspendedtherein.

Having now described an exemplary microfluidic device, a system forimplementing the method of the present invention is described withreference to FIG. 7. As is illustrated in the Figure, microfluidicdevice 200 includes a plurality of actuators 203 a-203 d. Microfluidicdevice 200 is of an appropriate geometry and is fitted with theappropriate actuation mechanism for carrying out a variety of objectcontrol tasks such as the electro-osmotic device previously described.

Microfluidic device 200 is coupled to sensor 730 by which the positionsof objects within the microfluidic device are located and the attributesof the objects may be ascertained. The present invention may beimplemented by any object sensor means capable of locating the objectsto within a desired accuracy. Such sensor means includes, but is notlimited to, microscopic cameras, fiber optics, electromagnetic sensorsand thermal sensors. The sensor should, of course, be appropriate todetermine the property of the object upon which control thereof isconditioned.

Coupling of the sensor 730 to microfluidic device 200 need not be aphysical connection (as indicated by the dashed line). For example,sensor 730 may be a digital camera fitted with optics appropriate toview the objects in microfluidic device 200. In certain embodiments ofthe present invention, the optics may be part of a microscope, thecamera being coupled to the ocular port thereof. In such embodiments, itshould be apparent that one or more of the plates 205, 207 ofmicrofluidic device 200 be transparent to provide optical access to theobjects in the microfluidic chamber 220. Images captured by the cameramay be processed by known image processing techniques to determine anobject's position, conformation, or other attribute, an exemplaryembodiment of which will be described in paragraphs below.

Actuators 203 a-203 d are respectively coupled to an amplifier ortransducer of amplifier/transducer stage 720. Amplifier/transducersection 720 converts electrical signals from computer 710, into signalsappropriate to the actuator type. For example, if actuators 203 a-203 dare driven by the pressure of a gas, amplifier/transducer section 720controls the gas pressure for each actuator responsive to an electricalsignal supplied by computer 710. In other embodiments, such as theelectro-osmotic device described hereinabove, amplifier/transducersection 720 conditions the electrical signal from computer 710 to anelectrical signal having an electric potential appropriate to thecorresponding actuator.

Computer 710 is configured as the controller of the system of FIG. 7.The computer 710 receives images from a sensor 730, processes thoseimages to determine the appropriate properties of the objects ofinterest in the microfluidic device 200, determines the correcttrajectory for each of the objects in accordance with the method of thepresent invention, and produces an output signal to amplifier/transducersection 720 so as to produce the current flow required to move theobjects along the corresponding trajectory. Note that whereas the systemof FIG. 7 is illustrated as a system of discrete components, the systemmay be constructed as a single, self-contained unit.

As is illustrated in FIG. 7, computer 710 forms the operational platformfor a system controller 715. It should be clear, however, that computer710 may perform other functions, such as providing a user interface tothe system, and such functions may be implemented by numerous methodswell-known in the art. Thus, only the details of system controller 715will be described further.

In certain embodiments of the present invention, system controller 715is implemented as a Time Varying Linear Quadratic Regulator (TVLQR) suchas is well-known in the optimal control art. The TVLQR may be adapted tocompensate for errors in position of the objects being controlled bysystem controller 715.

As was developed in paragraphs hereinabove, the desired position of anobject p_(D)(t+Δt) is set by an input to the actuators by therelationshipp _(D)(t+Δt)=A[p _(D)(t+Δt)]u(t+Δt)  (32)As is the case with any physical system, there will be errors in theobject's position after the actuation cycle has been completed. Thispositional error, denoted hereinafter as p_(E)(t), results fromshortcomings of the model to accurately portray the physical process ofthe fluid flow within the microfluidic device, deviations from nominalin the actual actuator signals, movement of the object through Brownianmotion, as well as other system noise sources.

If the position of the object is represented as a sum of the desiredposition and the positional error, i.e.,p _(T)(t)=p _(D)(t)+p _(E)(t),  (33)then the position of the object at some future time t+Δt is given by{dot over (p)} _(T)(t)=p _(D)(t)+p _(E)(t)+A[p _(D)(t+Δt)+p_(E)(t+Δt)][u _(D)(t+Δt)+u _(E)(t+Δt)]  (34)where,{dot over (p)} _(T)(t)=p _(T)(t+Δt).  (35)The vector u_(E)(t) represents the actuation signal that would bringabout the positional error p_(E)(t).

In a manner consistent with optimal control theory, the positional errorof the objects under control of system controller 715 may be modeled by{dot over (p)} _(E)(t)=F(t)p _(E)(t)+G(t)u _(E)(t)  (36)where F(t) and G(t) contain the coefficients to the differentialequation characterizing the error behavior of the open loop system.Using this model for the positional error, {dot over (p)}_(E)(t), it isdesired to correct the positional deviation from an initial non-zerostate p_(E)(t₀) to a final state p_(E)(t_(f))=0, where t_(f) is the timewithin which the positional error is to be extinguished. The correctiveactuation signal, u_(E)(t) can be found by minimizing the cost function$\begin{matrix}{J = {\int_{0}^{t_{f}}{\lbrack {{{p_{E}^{T}(t)}{Q(t)}{p_{E}(t)}} + {{u_{E}^{T}(t)}{R(t)}{u_{E}(t)}}}\quad \rbrack{\mathbb{d}t}}}} & (37)\end{matrix}$where Q(t) and R(t) are positive definite matrices and are chosen toinsure realizability of u_(E)(t) and p_(E)(t). The actuation signal thatsolves this optimization problem is known to be,u _(E)(t+Δt)=−K(t)p _(E)(t)  (38)where,K(t)=Q ⁻¹(t)G(t)S(t)  (39)The matrix S(t) is the solution to the Ricatti differential equation,{dot over (S)}(t)=−S(t)F(t)−F ^(T)(t)S(t)+S(t)G(t)R ⁻¹(t)G^(T)(t)S(t)−Q(t)  (40)S(t _(f))=0,  (41)where{dot over (S)}(t)=S(t+Δt)  (42)

A block diagram of an exemplary set of processing functions of computer710 is depicted in FIG. 8. The processing functions may be distributedacross multiple computing platforms or may be performed on a singlecomputing device. It should be clear to the skilled artisan that suchdistribution of functions is intended to fall within the scope of thepresent invention.

As shown at block 830 of FIG. 8, the desired trajectories for N objectscontained within the microfluidic chamber 220 are computed. Thetrajectories may be computed a priori and held within a table in memoryor may be computed dynamically as, for example, by user input to thesystem. In certain embodiments of the present invention, thetrajectories are maintained as a series of object positions at which theN objects are to be located at a given time period.

The desired trajectories are provided to actuation processor 840, whichdetermines the force field required to transport the N objects alongtheir respective trajectories. Actuation processor 840 provides at itsoutput a vector of actuation signals that, when applied to the actuationsystem of the microfluidic device, produces the computed force field.

At prescribed sampling intervals, an image of the microfluidic chamber220 is acquired via sensor 730 as shown at block 810. In certainembodiments of the present invention, the image data are in the form ofpixels, each having a value corresponding to physical properties of thefluid and objects suspended therein at the corresponding pixel location.For example, in the case where the image is constructed of optical data,the value of each pixel may correspond to optical transmissivity of thefluid (and objects suspended therein) at the location in themicrofluidic chamber 220 corresponding to the pixel location.

The captured image is transferred to image processor 820 by which the Nobjects are located and characterized. Any known image processingtechnique capable of isolating multiple objects of varying conformation,density, distribution, etc. may be utilized by the present invention andan exemplary embodiment will be described with reference to FIGS. 14-18.The results of the image processing function 820 should be the locationand characteristics of the N objects identified and corresponding to theN objects of block 830.

The actual object locations as determined by the image processor 820 arecompared with the desired trajectories computed at block 830 at summingnode 860, the output of which is a positional error for each of the Nobjects within the microfluidic chamber 220. The positional error foreach object is used to compute a corresponding corrective trajectory atblock 870. The corrective trajectory is one which is directed from theactual location of the corresponding object to its desired position. Thecorrective trajectories are provided to eigenmode processor 880 whichdetermines the underlying fluid flow to move each object along itscorrective trajectory and provides at its output the correspondingactuation signals. The actuation signals of eigenmode processor 840 andthose of eigenmode processor 880 are combined at summing node 850 toproduce a set of total actuation signals which are subsequently appliedto the actuators of the microfluidic device.

Referring now to FIG. 9, there is shown a control diagram of anexemplary TVLQR of the present invention. A vector containing thepositions at time t+Δt, as shown at block 910, is input to block 920 toproduce the actuation signal u_(D)(t+Δt) through the relationship ofEquation (33). The position vector p_(D)(t+Δt) is delayed by an amountΔt through delay unit 915 to produce the position vector p_(D)(t). Thedelayed position vector is used as a comparison for computing the errorposition as will be discussed presently.

Initially, Δt=0 and the actuation signal u_(D)(t) is applied to theactuators as described by block 930. At the next sampling period, i.e.,t+Δt (set by delay unit 935), the positions of all the objects in themicrofluidic chamber 220 are determined by the sensor 730 to produce aposition vector p_(T)(t). The output of summing node 945 is the errorposition vector p_(E)(t)=p_(T)(t)−p_(D)(t). The error position vector isapplied to the dynamic gain block 950 to produce the error actuationsignal for the next sample period, u_(E)(t+Δt). The error actuationsignal is applied to the desired actuation signal in subsequentoperations to produce the total actuation signal u_(T)(t+Δt), which isapplied to the actuation block 930.

Referring now to FIG. 10, there is shown a flow chart of the principalsteps of exemplary embodiments of the method of the present invention.Upon instantiation of the process at start block 1010, flow istransferred to block 1015 wherein the desired positions of objectswithin the microfluidic chamber 220 are determined either from aprecalculated table or by dynamic computation. It is then determined, atdecision block 1020, whether the objects are in the final destinationand, if so, the method is terminated at exit block 1070. If it isdetermined that the objects are not in their respective final positions,flow is transferred to block 1025 by which an image of the microfluidicchamber 220 is captured by sensor 730. At block 1030, the actual objectpositions are determined by image processing, as shown at block 1030.The positional error of each of the objects is determined at block 1035.

At block 1040, the Ricatti differential equation is solved for S(t). Incertain embodiments of the present invention, such as when the objecttrajectories have been precalculated prior to the instantiation of themethod, the solution for S(t) may be determined off-line and stored foreach of a plurality of predetermined regions of microfluidic chamber220. The regions for which S(t) are solved are determined in accordancewith its adjacency to each object trajectory.

Once a solution for the Ricatti differential equation has been computedin block 1040, flow is transferred to block 1045 in which the feedbackgain K(t) is computed. Once again, values for K(t) may be computedoff-line when the object trajectories were predetermined.

In block 1050, a corrective actuation signal is computed from thepositional error of each object and, in block 1055, an open loopactuation signal is determined from the desired object position. Itshould be clear to one of ordinary skill in the art, that the order inwhich the corrective voltage and the open loop voltage are computed doesnot affect the outcome of the method of the present invention.

As shown at block 1060, the total actuation signal is computed as thesum of the open loop actuation signal and the corrective actuationsignal and is applied to the actuators of the microfluidic device. Flowis transferred to block 1065 at which it is determined if the nextsample period has arrived. If not, the method is suspended until thenext sample period. Once the next cycle time has arrived, the methodrepeats at block 1015 until each object is in its final position asdetermined at block 1020.

FIGS. 11A-11D illustrate, in time sequence, the motion of four particleswithin the exemplary electro-osmotic microfluidic device describedabove. In each figure, the arrows indicate a fluid flow vectorassociated with the sum of eigenmodes applied to the device and theisobars indicate levels of constant pressure. As is illustrated in theFigures, motion of the four particles may be independently controlledvia the underlying current flow of the fluid in the microfluidic chamber220.

Referring now to FIG. 14, there is shown an exemplary sensing system forimplementing certain embodiments of the present invention. As is shownin the Figure, a digital camera 1440 is optically coupled to amicroscope 1430 at the ocular port thereof. The microscope 1430 isfocused on the microfluidic chamber of microfluidic device 200. Thecamera/microscope serves as image capturing system for the sensor.Subsequent image processing may configure the sensor as a positionsensor for locating the positions of objects in the microfluidic device200, as an object recognition sensor for distinguishing objects havingdifferent attributes from one another, as an object conformation sensorfor determining the conformation of an object, and as an objectdistribution sensor for determining the positions of different segmentsof distributed objects. Other characteristics of objects may beascertained as determined by the image processing technique deployed.The sensor is coupled to computer 710 which supplies the actuationsignal determined from the output of the sensor as discussedhereinabove.

In certain embodiments of the present invention, an image captured bycamera 1440 is passed through a threshold filter to convert the image toa binary form. As is shown in FIG. 15, a histogram of image pixel valuesis maintained over time and a center value is chosen for a threshold,thr. The center may be found by simple means, such as by finding anumerical average between minimum and maximum values in the histogram,or may be found by more complex statistical analysis. The binary imageoutput by the threshold filter contains a one (1), for example, at pixellocations where the original pixel value is above the threshold valueand a zero (0), for example, at pixel locations where the original pixelvalue is below the threshold value.

As shown in FIG. 16, the binary image produced by the threshold filterconsists of binary-valued pixels. In order to process the image withsufficient speed so as to control the objects in near real-time, certainembodiments of the present invention converts the image to a run lengthcode (RLC) representation thereof, such as is well known in the art. TheRLC representation reduces significantly the data that requires furtherprocessing. The RLC for an image consists of a series of number pairs.The first number of the pair indicates the column in which an image bitis set and the second number indicates how many consecutive image bitsin the current row from the current image position are set. For example,the RLC for the image of FIG. 16 may be given by the series (3,4), (2,6), ((1, 2), (7, 2)), ((1, 2), (7, 2)), (2, 6), (3, 4).

An exemplary image processing method is illustrated by way of the flowchart of FIG. 18. In block 1810, image regions of a present image inwhich objects are to be located are identified. This may be achieved bypredictive techniques or may be accomplished by simple block processingknown in the art. A previously obtained image is recalled in block 1830and supplied to produce reference image 1820. The reference image 1820,in certain embodiments, is predicted from the previously obtained imageto provide an estimate of the present image. The present image and thereference image are subtracted, as indicated at block 1840, to produce adifferential image in which areas of greater difference are lighter thanthose areas of lesser difference. The differential image is passedthrough a threshold filter, such as described above, as shown at block1850. The resulting binary image is converted to an RLC representationthereof, as shown at block 1860 and objects are detected at block 1870.The position and characteristics of ring objects as detected within amicrofluidic chamber is shown in FIG. 17.

Once the objects have been detected, they may be identified anddistinguished from one another by attribute. Each object may then belabeled, as shown at block 1880, by attribute or as an object previouslyidentified, such as for purposes of object tracking. The positions ofthe center of the objects are identified in block 1890 and aretransmitted to the object control algorithm. The object position may bedetermined by known techniques in the image processing art.

By way of the method of the present invention, operations on severaldifferent types of objects may be accomplished, as shown in FIGS. 12a-12 d. FIG. 12 a illustrates a sorting operation by which a variety ofobjects are sorted to corresponding sorting bin locations 1210 a-1210 d.In FIG. 12B, there is illustrated an example of the method of thepresent invention used to steer a pair of particles into one another. InFIG. 12C, an amount of fluid comprising 18% of a total amount of fluidis separated from a volume of fluid. This is accomplished by segmentingthe fluid boundaries into discrete object locations, such as 1230 and1235, and directing those locations toward each other as shown. Thus,the objects being manipulated by the present invention need notnecessarily be distinct, but may be a segment of a larger structure. Inlike manner, FIG. 12D illustrates manipulation of stranded structures,such as DNA chains. The strand is segmented into a plurality of segmentobjects 1240 a-1240 j and the objects are conducted along trajectoriesto conform the strand as needed.

FIGS. 13A and 13B illustrate a particular example of an experiment thatmight be conducted by means of the present invention. In FIG. 13A, afluid B, located at 1310, is surrounded by a fluid A and has suspendedtherein a plurality of particles 1320 a-1320 d. Fluid B may bechemically altered by objects 1320 a and 1320 d, wherein the amount ofalteration is the quantity to be studied. After a predetermined periodof time, it may be desired that fluid B be removed from all particles ofthe type of particles 1320 a-1320 d and to be moved to contact objects1330 a-1330 j. Objects 1330 a-1330 j may respond to the chemicals understudy. Objects 1330 a-1330 j, in subsequent steps, may be moved via themethod of the present invention to a collection location for analysis.

Although the invention has been described herein in conjunction withspecific embodiments thereof, many alternatives, modifications, andvariations will be apparent to those skilled in the art. The presentinvention is intended to embrace all such alternatives, modifications,and variations that fall within the spirit and broad scope of theappended claims.

1. A method for transporting a plurality of particles suspended in afluid contained by a microfluidic receptacle respectively along acorresponding one of a plurality of trajectories, the microfluidicreceptacle having adapted thereto a plurality of actuators forrespectively applying a corresponding force on each of the plurality ofparticles, the method comprising the steps of: (a) providing themicrofluidic receptacle with a particle position sensor for detecting apresent position of each of the plurality of particles; (b) determininga plurality of force fields for the microfluidic receptacle, each ofsaid plurality of force fields established responsive to a respectiveset of actuation signals being applied to the plurality of actuators;(c) selecting a destination point on each of the plurality oftrajectories to which the corresponding particle is to be moved within apredetermined time interval; (d) determining a first plurality of forcesto be respectively applied to a corresponding one of the plurality ofparticles so as to move each of the plurality of particles to saidcorresponding destination point within said predetermined time interval;(e) selecting a first set of said plurality of force fields producingsaid first plurality of forces; (f) applying said actuation signalscorresponding to said set of force fields to said plurality ofactuators; (g) determining said present position of each of theplurality of particles in the microfluidic receptacle via said particleposition sensor; (h) calculating a positional error of said presentposition from said corresponding destination point for each of theplurality of particles; (i) determining a second plurality of forces tobe respectively applied to a corresponding one of the plurality ofparticles so as to move each of the plurality of particles from saidcorresponding present position to said corresponding destination pointwithin said predetermined time interval if said positional error exceedsa predetermined positional error tolerance; (j) selecting a second setof said plurality of force fields producing second plurality of forces;(k) applying said actuation signals corresponding to said second set offorce fields to said plurality of actuators; and (l) repeating themethod at said step (c) until each of the plurality of particles hasrespectively traversed the corresponding one of the plurality oftrajectories.
 2. The method for transporting a plurality of particlesalong a corresponding one of a plurality of trajectories as recited inclaim 1, whereby said particle position sensor providing step (a)includes the step of providing said particle position sensor with animage capture device for obtaining an image of the plurality ofparticles in the microfluidic receptacle.
 3. The method for transportinga plurality of particles along a corresponding one of a plurality oftrajectories as recited in claim 2, whereby said present positiondetermining step (g) includes the steps of: (1) obtaining an image ofthe plurality of particles in the microfluidic receptacle; (2)identifying the plurality of particles in said image; and (3)identifying said present position for each of the plurality of particlesfrom said image.
 4. The method for transporting a plurality of particlesalong a corresponding one of a plurality of trajectories as recited inclaim 3 further comprising the step of providing each of the pluralityof actuators with a corresponding one of a plurality of electrodes. 5.The method for transporting a plurality of particles along acorresponding one of a plurality of trajectories as recited in claim 4,whereby the plurality of force fields are respective electric fieldsestablished between said plurality of electrodes.
 6. The method fortransporting a plurality of particles along a corresponding one of aplurality of trajectories as recited in claim 7, whereby said actuationsignal application step (f) includes the steps of: (1) determining avoltage corresponding to each of said actuation signals; and (2)applying said voltage respectively to a corresponding one of saidplurality of electrodes.
 7. The method for transporting a plurality ofparticles along a corresponding one of a plurality of trajectories asrecited in claim 6, whereby said actuation signal application step (k)includes the steps of: (1) determining a voltage corresponding to eachof said actuation signals; and (2) applying said voltage respectively toa corresponding one of said plurality of electrodes.
 8. A method fortransporting a plurality of particles suspended in a fluid contained bya microfluidic receptacle respectively along a corresponding one of aplurality of trajectories, the microfluidic receptacle having adaptedthereto a plurality of fluid actuators for respectively applying acorresponding force on the fluid, the method comprising the steps of:(a) determining a plurality of fluid flow fields for the microfluidicreceptacle, each of said plurality of fields defining a fluid flowresponsive to a respective set of actuation signals being applied to theplurality of fluid actuators; (b) selecting a destination point on eachof the plurality of trajectories to which the corresponding particle isto be moved within a predetermined time interval; (c) selecting a firstset of said plurality of fluid flow fields producing a fluid flow forrespectively transporting each of the plurality of particles to saiddestination point on said corresponding trajectory within saidpredetermined time interval; (d) applying said actuation signalscorresponding to said set of fluid flow fields to said plurality offluid actuators; and (e) repeating the method at said step (b) untileach of the plurality of particles has respectively traversed thecorresponding one of the plurality of trajectories.
 9. The method fortransporting a plurality of particles along a corresponding one of aplurality of trajectories as recited in claim 8, further including thesteps of: (f) providing the microfluidic receptacle with a particleposition sensor for detecting a present position of each of theplurality of particles; (g) determining said present position of each ofthe plurality of particles in the microfluidic receptacle via saidparticle position sensor; (h) prior to said method repeating step (g),performing the steps of: (1) calculating a positional error of saidpresent position from said corresponding destination point for each ofthe plurality of particles; and (2) selecting a second set of saidplurality of fluid flow fields producing a fluid flow for respectivelytransporting each of the plurality of particles from said correspondingpresent position to said destination point on said correspondingtrajectory within said predetermined time interval if said positionalerror exceeds a predetermined positional error tolerance; and (i) addingto said actuation signals applied in step (f) said actuation signalscorresponding to said second set of fluid flow fields.
 10. The methodfor transporting a plurality of particles along a corresponding one of aplurality of trajectories as recited in claim 9, whereby said positionalerror is determined by subtracting said present position correspondingto each of the plurality of particles from said destination point onsaid corresponding trajectory.
 11. The method for transporting aplurality of particles along a corresponding one of a plurality oftrajectories as recited in claim 9, whereby said particle positionsensor providing step (f) includes the step of providing said particleposition sensor with an image capture device for obtaining an image ofthe plurality of particles in the microfluidic receptacle.
 12. Themethod for transporting a plurality of particles along a correspondingone of a plurality of trajectories as recited in claim 11, whereby saidpresent position determining step (g) includes the steps of: (1)obtaining an image of the plurality of particles in the microfluidicreceptacle; (2) identifying the plurality of particles in said image;and (3) identifying said present position for each of the plurality ofparticles from said image.
 13. The method for transporting a pluralityof particles along a corresponding one of a plurality of trajectories asrecited in claim 12 further including the steps of: (j) providing themicrofluidic receptacle with two parallel plates separated by apredetermined separation distance, said parallel plates defining amicrofluidic chamber therebetween; and (k) providing each of theplurality of fluid actuators with a corresponding one of a plurality ofelectrodes, said electrodes being installed on an outer periphery ofsaid microfluidic chamber.
 14. The method for transporting a pluralityof particles along a corresponding one of a plurality of trajectories asrecited in claim 13, whereby said actuation signal application step (d)includes the steps of: (1) determining a voltage corresponding to eachof said actuation signals; and (2) applying said voltage respectively toa corresponding one of said plurality of electrodes.
 15. The method fortransporting a plurality of particles along a corresponding one of aplurality of trajectories as recited in claim 14 further including thesteps of: (l) providing at least one of said parallel plates with atransparent region such that said microfluidic chamber therethrough; (m)providing said image capture device with an optical camera mounted on anocular port of a microscope; (n) focusing said microscope on saidmicrofluidic chamber; and (O) obtaining a photographic image as saidimage in said present position determining step (g).
 16. The method fortransporting a plurality of particles along a corresponding one of aplurality of trajectories as recited in claim 15, whereby said particleidentifying step (2) in said present position determining step (g)further includes the steps of: (a) applying an image transformation tosaid photographic image for locating contours of objects within saidmicrofluidic chamber; and (b) identifying one of said objects as one ofsaid plurality of particles if said contour of said object correspondsto a characteristic of said plurality of particles.
 17. A method forsorting a plurality of particles suspended in a fluid contained by amicrofluidic receptacle, the microfluidic receptacle having adaptedthereto a plurality of fluid actuators for respectively applying acorresponding force on the fluid, the particles being respectivelysorted to a sorting bin location in accordance with a correspondingattribute, the method comprising the steps of: (a) determining aplurality of fluid flow fields for the microfluidic receptacle, each ofsaid plurality of fields defining a flow responsive to a respective setof actuation signals being applied to the plurality of fluid actuators;(b) providing the microfluidic receptacle with a particle recognitionsensor adapted to respectively detect a present position and anattribute of each of the plurality of particles within the fluid; (c)determining said present position and said attribute of each of theplurality of particles in the microfluidic receptacle via said particlerecognition sensor; (d) determining a trajectory for each of saidplurality of particles, said trajectory directed from said presentposition and directed toward one of the plurality of sorting binlocations corresponding to said respective attribute; (e) determining arespective destination point on said trajectory to which thecorresponding particle is to be moved within a predetermined timeinterval; (f) selecting a set of said fluid flow fields producing afluid flow for respectively transporting each of the plurality ofparticles to said destination point within said predetermined timeinterval; (g) applying said actuation signals corresponding to said setof fluid flow fields to said plurality of fluid actuators; and (h)repeating the method at said step (c) until each of the plurality ofparticles has respectively arrived at said corresponding one of saidplurality of sorting bin locations.
 18. The method for sorting aplurality of particles as recited in claim 17, further including thesteps of: (i) prior to said method repeating step (h), performing thesteps of: (1) calculating a positional error of said present positionfrom said corresponding destination point for each of the plurality ofparticles; and (2) selecting a second set of said plurality of fluidflow fields producing a fluid flow for respectively transporting each ofthe plurality of particles from said corresponding present position tosaid destination point on said trajectory within said predetermined timeinterval if said positional error exceeds a predetermined positionalerror tolerance; and (j) adding to said actuation signals applied instep (g) said actuation signals corresponding to said second set offluid flow fields.
 19. The method for sorting a plurality of particlesas recited in claim 18, whereby said positional error is determined bysubtracting said present position corresponding to each of the pluralityof particles from said destination point on said correspondingtrajectory.
 20. The method for sorting a plurality of particles asrecited in claim 18, whereby said particle recognition sensor providingstep (b) includes the step of providing said particle position sensorwith an image capture device for obtaining an image of the plurality ofparticles in the microfluidic receptacle.
 21. The method for sorting aplurality of particles as recited in claim 20, whereby said presentposition and attribute determining step (c) includes the steps of: (1)obtaining an image of the plurality of particles in the microfluidicreceptacle; (2) identifying the plurality of particles in said image;and (3) identifying said present position and said attribute for each ofthe plurality of particles from said image.
 22. The method for sorting aplurality of particles as recited in claim 21 further including thesteps of: (k) providing the microfluidic receptacle with two parallelplates separated by a predetermined separation distance, said parallelplates defining a microfluidic chamber therebetween; and (l) providingeach of the plurality of fluid actuators with a corresponding one of aplurality of electrodes, said electrodes being installed on an outerperiphery of said microfluidic chamber.
 23. The method for sorting aplurality of particles as recited in claim 22, whereby said actuationsignal application step (g) includes the steps of: (1) determining avoltage corresponding to each of said actuation signals; and (2)applying said voltage respectively to a corresponding one of saidplurality of electrodes.
 24. The method for sorting a plurality ofparticles as recited in claim 23 further including the steps of: (m)providing at least one of said parallel plates with a transparent regionsuch that said microfluidic chamber therethrough; (n) providing saidimage capture device with an optical camera mounted on an ocular port ofa microscope; (o) focusing said microscope on said microfluidic chamber;and (p) obtaining a photographic image as said image in said presentposition and attribute determining step (c).
 25. The method for sortinga plurality of particles as recited in claim 24, whereby said particleidentifying step (2) in said present position and attribute determiningstep (c) further includes the steps of: (a) applying an imagetransformation to said photographic image for locating contours ofobjects within said microfluidic chamber; (b) identifying one of saidobjects as one of said plurality of particles if said contour of saidobject corresponds to a characteristic of said plurality of particles;and (c) determining said attribute of each of said plurality ofparticles from an optical characteristic thereof from said photographicimage.
 26. A method for conforming a strand from a first conformation toa second conformation, the strand being suspended in a fluid containedby a microfluidic receptacle, the microfluidic receptacle having adaptedthereto a plurality of fluid actuators for respectively applying acorresponding force on the fluid, the method comprising the steps of:(a) determining a plurality of fluid flow fields for the microfluidicreceptacle, each of said plurality of fields defining a flow responsiveto a respective set of actuation signals being applied to the pluralityof fluid actuators; (b) providing the microfluidic receptacle with astrand conformation sensor adapted to respectively detect a presentposition of a plurality of strand segments, said plurality of strandsegments defining the first conformation of the strand within the fluid;(c) determining said present position of each said plurality of strandsegments via said strand orientation sensor; (d) determining atrajectory for each of said plurality of strand segments, saidtrajectory directed from said present position and directed toward acorresponding one of a plurality of strand segment destinationlocations, said plurality of strand segment destination locationsdefining the second conformation of the strand; (e) determining arespective destination point on said trajectory to which thecorresponding strand segment is to be moved within a predetermined timeinterval; (f) selecting a set of said fluid flow fields producing afluid flow for respectively transporting each of the plurality of strandsegments to said destination point within said predetermined timeinterval; (g) applying said actuation signals corresponding to said setof fluid flow fields to said plurality of fluid actuators; and (h)repeating the method at said step (c) until each of said plurality ofstrand segments has respectively arrived at a corresponding one of saidplurality of strand segment destination locations.
 27. The method forconforming a strand from a first conformation to a second conformationas recited in claim 26, further including the steps of: (i) prior tosaid method repeating step (h), performing the steps of: (1) calculatinga positional error of said present position from said correspondingdestination point for each of the plurality of strand segments; and (2)selecting a second set of said plurality of fluid flow fields producinga fluid flow for respectively transporting each of the plurality ofstrand segments from said corresponding present position to saiddestination point on said trajectory within said predetermined timeinterval if said positional error exceeds a predetermined positionalerror tolerance; and (j) adding to said actuation signals applied instep (g) said actuation signals corresponding to said second set offluid flow fields.
 28. The method for conforming a strand from a firstconformation to a second conformation as recited in claim 27, wherebysaid positional error is determined by subtracting said present positioncorresponding to each of the plurality of strand segments from saiddestination point on said corresponding trajectory.
 29. The method forconforming a strand from a first conformation to a second conformationas recited in claim 27, whereby said strand conformation sensorproviding step (b) includes the step of providing said strandconformation sensor with an image capture device for obtaining an imageof the plurality of strand segments in the microfluidic receptacle. 30.The method for conforming a strand from a first conformation to a secondconformation as recited in claim 29, whereby said present positiondetermining step (c) includes the steps of: (1) obtaining an image ofthe plurality of strand segments in the microfluidic receptacle; (2)identifying the plurality of strand segments in said image; and (3)identifying said present position for each of the plurality of strandsegments from said image.
 31. The method for conforming a strand from afirst conformation to a second conformation as recited in claim 30further including the steps of: (k) providing the microfluidicreceptacle with two parallel plates separated by a predeterminedseparation distance, said parallel plates defining a microfluidicchamber therebetween; and (l) providing each of the plurality of fluidactuators with a corresponding one of a plurality of electrodes, saidelectrodes being installed on an outer periphery of said microfluidicchamber.
 32. The method for conforming a strand from a firstconformation to a second conformation as recited in claim 31, wherebysaid actuation signal application step (g) includes the steps of: (1)determining a voltage corresponding to each of said actuation signals;and (2) applying said voltage respectively to a corresponding one ofsaid plurality of electrodes.
 33. The method for conforming a strandfrom a first conformation to a second conformation as recited in claim32 further including the steps of: (m) providing at least one of saidparallel plates with a transparent region such that said microfluidicchamber therethrough; (n) providing said image capture device with anoptical camera mounted on an ocular port of a microscope; (o) focusingsaid microscope on said microfluidic chamber; and (p) obtaining aphotographic image as said image in said present position determiningstep (c).
 34. The method for conforming a strand from a firstconformation to a second conformation as recited in claim 33, wherebysaid strand segment identifying step (2) in said present position andattribute determining step (c) further includes the steps of: (a)applying a watershed image transformation to said photographic image forlocating contours of objects within said microfluidic chamber; and (b)identifying one of said objects as one of said plurality of strandsegments if said contour of said object corresponds to a characteristicof said plurality of strand segments.
 35. A method for redistributing afirst volume of fluid from a first distribution to a seconddistribution, the first volume of fluid being contained within a secondvolume of fluid and being separated therefrom by at least one interface,said second volume of fluid contained by a microfluidic receptacle, themicrofluidic receptacle having adapted thereto a plurality of fluidactuators for respectively applying a corresponding force on the fluid,the method comprising the steps of: (a) determining a plurality of fluidflow fields for the microfluidic receptacle, each of said plurality offields defining a flow responsive to a respective set of actuationsignals being applied to the plurality of fluid actuators; (b) providingthe microfluidic receptacle with a fluid distribution sensor adapted torespectively detect a present position of a plurality of interfacesegments, said plurality of interface segments defining the interfacebetween the first volume of fluid and the second volume of fluid; (c)determining said present position of each said plurality of interfacesegments via said fluid distribution sensor; (d) determining atrajectory for each of said plurality of interface segments, saidtrajectory directed from said present position and directed toward acorresponding one of a plurality of interface segment destinationlocations, said plurality of interface segment destination locationsdefining the second distribution of the first volume of fluid; (e)determining a respective destination point on said trajectory to whichthe corresponding interface segment is to be moved within apredetermined time interval; (f) selecting a set of said fluid flowfields producing a fluid flow for respectively transporting each of theplurality of interface segments to said destination point within saidpredetermined time interval; (g) applying said actuation signalscorresponding to said set of fluid flow fields to said plurality offluid actuators; and (h) repeating the method at said step (c) untileach of said plurality of interface segments has respectively arrived ata corresponding one of said plurality of interface segment destinationlocations.
 36. The method for redistributing a first volume of fluidfrom a first distribution to a second distribution as recited in claim35, further including the steps of: (i) prior to said method repeatingstep (h), performing the steps of: (1) calculating a positional error ofsaid present position from said corresponding destination point for eachof the plurality of interface segments; and (2) selecting a second setof said plurality of fluid flow fields producing a fluid flow forrespectively transporting each of the plurality of interface segmentsfrom said corresponding present position to said destination point onsaid trajectory within said predetermined time interval if saidpositional error exceeds a predetermined positional error tolerance; and(j) adding to said actuation signals applied in step (g) said actuationsignals corresponding to said second set of fluid flow fields.
 37. Themethod for redistributing a first volume of fluid from a firstdistribution to a second distribution as recited in claim 36, wherebysaid positional error is determined by subtracting said present positioncorresponding to each of the plurality of interface segments from saiddestination point on said corresponding trajectory.
 38. The method forredistributing a first volume of fluid from a first distribution to asecond distribution as recited in claim 36, whereby said fluiddistribution sensor providing step (b) includes the step of providingsaid fluid distribution sensor with an image capture device forobtaining an image of the plurality of interface segments in themicrofluidic receptacle.
 39. The method for redistributing a firstvolume of fluid from a first distribution to a second distribution asrecited in claim 38, whereby said present position determining step (c)includes the steps of: (1) obtaining an image of the plurality ofinterface segments in the microfluidic receptacle; (2) identifying theplurality of interface segments in said image; and (3) identifying saidpresent position for each of the plurality of interface segments fromsaid image.
 40. The method for redistributing a first volume of fluidfrom a first distribution to a second distribution as recited in claim39 further including the steps of: (k) providing the microfluidicreceptacle with two parallel plates separated by a predeterminedseparation distance, said parallel plates defining a microfluidicchamber therebetween; and (l) providing each of the plurality of fluidactuators with a corresponding one of a plurality of electrodes, saidelectrodes being installed on an outer periphery of said microfluidicchamber.
 41. The method for redistributing a first volume of fluid froma first distribution to a second distribution as recited in claim 40,whereby said actuation signal application step (g) includes the stepsof: (1) determining a voltage corresponding to each of said actuationsignals; and (2) applying said voltage respectively to a correspondingone of said plurality of electrodes.
 42. The method for redistributing afirst volume of fluid from a first distribution to a second distributionas recited in claim 41 further including the steps of: (m) providing atleast one of said parallel plates with a transparent region such thatsaid microfluidic chamber therethrough; (n) providing said image capturedevice with an optical camera mounted on an ocular port of a microscope;(o) focusing said microscope on said microfluidic chamber; and (p)obtaining a photographic image as said image in said present positiondetermining step (c).
 43. The method for redistributing a first volumeof fluid from a first distribution to a second distribution as recitedin claim 42, whereby said interface segment identifying step (2) in saidpresent determining step (c) further includes the steps of: (a) applyingan image transformation to said photographic image for locating contoursof objects within said microfluidic chamber; and (b) identifying one ofsaid objects as one of said plurality of interface segments if saidcontour of said object corresponds to a characteristic of said pluralityof interface segments.